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EleoNora [17]
3 years ago
9

In science class, Jada uses a graduated cylinder with water in it to measure the volume of some marbles. After dropping in 4 mar

bles so they are all under water, the water in the cylinder is at a height of 10 milliliters. After dropping in 6 marbles so they are all under water, the water in the cylinder is at a height of 11 milliliters.
If this can be represented by a liner model, predict the height of the cylinder after dropping in 8 marbles.
Mathematics
1 answer:
sertanlavr [38]3 years ago
8 0

Answer:

The height of water in the cylinder after drooping 8 marbles is 12 mm

Step-by-step explanation:

∵ The change of the height of the water varies directly with the change of the  number of marbles

∵ (h2 - h1) α (x2 - x1)

∴ (h2 - h1) = k (x2 - x1)

∴ (11 - 10) = k (6 - 4)

∴ 1 = 2 k

∴ k = 1/2

∴ (h2 - h1) = 1/2 (x2 - x1)

∴ (Δh) = 1/2 (Δx)

∴ h3 - 11 = 1/2 (8 - 6)

∴ h3 = 1/2 × 2 + 11 = 12 milliliter

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Given that WA = 5x – 8 and WC = 3x + 2, find WB. A. WB = 5 B. WB = 8 C. WB = 10 D. WB = 17
rodikova [14]
The rest of the question is the attached figure.
============================================
Δ AYW a right triangle at Y ⇒⇒⇒ ∴ WA² = AY² + YW²
And AY = YB ⇒⇒⇒ ∴ WA² = YB² + YW²   → (1)
Δ BYW a right triangle at Y ⇒⇒⇒ ∴ WB² = BY² + YW²  → (2)
From (1) , (2)  ⇒⇒⇒ ∴ WA = WB  →→ (3)
Δ CXW a right triangle at Y ⇒⇒⇒ ∴ WC² = CX² + XW²
And CX = XB ⇒⇒⇒ ∴ WC² = XB² + XW²   → (4)
Δ BXW a right triangle at Y ⇒⇒⇒ ∴ WB² = XB² + XW²  → (5)
From (4) , (5)  ⇒⇒⇒ ∴ WC = WB  →→ (6)
From (3) , (6)
WA = WB = WC
given ⇒⇒⇒ WA = 5x – 8 and WC = 3x + 2
∴ <span> 5x – 8 = 3x + 2</span>
Solve for x ⇒⇒⇒ ∴ x = 5
∴ WB = WA = WC = 3*5 + 2 = 17

The correct answer is option D. WB = 17






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